optimum brightness level and simplified characterization of crt color monitors

Optimum Brightness Level andSimplified Characterization ofCRT Color Monitors

Park Seung–ok,* Kim Hong–suk,Baek Jung–kiDept. of Physics, Daejin University, Kyungki–Do, Korea

Received 10 August 1999; accepted 23 December 1999

Abstract: The nonlinear relationship between luminanceand DAC count could be characterized with the simplifiedmodel, if optimum brightness level is set. In this study, wepropose a technique to set the optimum level of brightness,in which offsets for RGB channels can be assumed to zero,and determine the gamma coefficients from log–log datawithout nonlinear optimization. The optimum brightnesslevel could be found by measuring a few tones of neutral forthe combination of 3 levels of brightness and 2 levels ofcontrast. This technique has two advantages. It does notrequire measurements for 0 DAC count, and does not re-quire nonlinear optimization in finding the gamma coeffi-cient of the display system. Two CRT monitors by differentmanufacturers have been tested. As the result, all monitorscould be set to their optimum state with a different combi-nation of brightness and contrast. In that state, the gammacoefficient for each channel could be determined from twomeasuring data and the tone reproduction characteristics ofthe RGB channel could be characterized with the simplifiedequation, neglecting offset and gain. The accuracy of char-acterization was better than 0.5DE*ab for 125 colors for amonitor having good channel independence.© 2000 John

Wiley & Sons, Inc. Col Res Appl, 25, 408–415, 2000

Key words: CRT color monitor; optimum brightness level;simplified characterization; gamma coefficient

INTRODUCTION

As the cost of computer display systems has decreased, theuse of color displays has increased. One of the color dis-

plays most commonly used is the CRT color monitor. CRTcolor monitors are widely used to visualize graphic design,to produce visual stimuli, for soft proofing, and so on1-3.

CRT color monitors produce an image with the lightsemitted by red, green, and blue phosphor. The quality of theimage depends on the nonlinear relationship between theamount of emitted light and the DAC count applied to RGBchannels. The traditional CRT techniques have been sum-marized by Berns and can be described as the gain-offset-gamma (GOG) model to characterize this nonlinear rela-tionship.4-5

However, most practitioners in computer graphics preferto use the simplified model including only the gammacoefficient. Also, many software packages attempting colorWYSIWYG have been made on the simplified relationship.However, the simplified model is correct only for a partic-ular setup; the normalized gain equals unity and the nor-malized offset equals zero. In fact, this particular setupoccurs very infrequently in practice.

The objective of this study is to achieve that particularsetup by using brightness and contrast controls. In mostmonitors, brightness and contrast vary the offsets and gainsof all three channels simultaneously. Many researchers havestudied the effects of brightness and contrast on the repro-duced image.6-8 Brightness affects mainly the minimumluminance of black, and contrast affects mainly the maxi-mum luminance of RGB primaries. Recently, the influenceof brightness and contrast in the color reproduction has beenquantified. Researchers reported that a medium or minimumbrightness level in the combination of high contrast is theoptimum setting for a monitor.9 To adjust a particular setup,in which offsets for all channels are assumed to be zero, itis necessary to define optimum brightness level more accu-rately.

In this article, we propose a technique to set the optimum

* Correspondence to: Seung–ok Park, Dept. of Physics, Daejin Univer-sity, Kyungki–Do, Korea (e-mail: [email protected])

Contract grant sponsor: Center for Educational–Industrial Cooperationof Daejin University© 2000 John Wiley & Sons, Inc.

408 COLOR research and application

brightness level and show the accuracy of characterizationusing the simplified model.

THEORETICAL BASIS

The relationship between luminance and normalized DACcount, known astone reproduction characteristics, has beenrepresented by the GOG model as follows5:

L 5 Fb 1 aS d

2N 2 1DGg

, (1)

whered is the DAC count,b is the amplifier offset,a is theamplifier gain, andg is the inherent coefficient of thedisplay system, depending on the properties of the particularcathode-ray tube.

As the amplifier gain and offset vary, the tone reproductioncharacteristics of the monitor change. Figure 1 shows theluminance vs. DAC count for 5 amplifier offsets:b 5 21.0,20.5, 0, 0.5, 1.0, with a fixed gain and gamma based onenumerating Eq. (1). As the offset becomes higher, the wholecurve raises. However, the pronounced difference is at thelower DAC count, near 0. For the negative offset, the lumi-nance curve terminates abruptly at zero luminance before 0DAC count. And, for the positive offset, the luminance of 0DAC is above 0, which means that no input counts display thetrue black. This aspect is clearer in the log-luminance vs.log-DAC count of Fig. 2. The sign of curvature is oppositebetween the negative and positive offset. As the absolute valueof the offset decreases, the radius of curvature becomes larger,and then, for 0 offset, the curved line becomes a straight line.

In Eq. (1), the normalized luminance divided by its max-imum shown in Fig. 3 can be expressed as follows:

L

Lmax5

Sb 1 ad

2N 2 1Dg

~b 1 a!g . (2)

For an arbitrary luminance ratio ofA, DAC counts satisfingEq. (2) can be solved as

d 5~2N 2 1!

a@A1/g~a 1 b! 2 b#

5b

a~2N 2 1!~ A1/g 2 1! 1 ~2N 2 1! A1/g (3)

5b

a~2N 2 1!~ A1/g 2 1! 1 d0,

where

d0 5 ~2N 2 1! A1/g

represents the relationship between DAC count andA, whenb 5 0. This equation means that the relationship betweenthe DAC count and the offset is linear, and the ratio of theproportion is inversely proportional to the gain. For a con-stant gain, the plot of the DAC count yields an arbitraryvalue ofA vs. the offset is, therefore, a straight line havingan intercept ofd0. In addition, the lines obtained fromdifferent gains are crossed at their common intercept.

For example, the DAC counts that yield constantA of0.25 vs. the offset for three gains are shown in Fig. 4. Eachgain setting shows a straight line whose slope is inverselyproportional to the gain as expected. And all lines havingdifferent slopes cross atd0, where the offset is 0. Therefore,0 offset can be defined from that intersection point.

Usually, a CRT color monitor has brightness and contrastcontrols, which control the offsets and gains (respectively)of the RGB channels simultaneously. Therefore, by settingthe optimum brightness control, the offsets of RGB chan-

FIG. 1. Luminance vs. DAC count for 5 different amplifieroffset settings, when gain and gamma are fixed.

FIG. 2. Log-luminance vs. log-DAC count for 5 differentamplifier offset settings, when gain and gamma are fixed.

Volume 25, Number 6, December 2000 409

nels can be adjusted to their minimum values simulta-neously. Following the above theoretical basis, the optimumbrightness level could be found from the four settings com-bined with the two levels of brightness and two levels ofcontrast.

However, in the actual monitor, tone reproduction char-acteristics are not represented with the inherent gammacoefficient of the display system in Eq. (1). As the bright-ness and contrast vary,g is changed, as well as offset andgain. The change ing would bring nonlinearity to therelationship between DAC count and brightness level. Thisproblem must be considered previously before selectingbrightness and contrast levels.

MEASUREMENTS

Two CRT monitors form different manufactures have beentested. One is LG Flatron 795 FT Plus and the other isSamsung SyncMaster 700P. All monitors were set to theD65 white point, 10243 768 at 85 Hz, and 24-bit full colorresolution. They were driven using the same video card(ATI Rage Fury 128). The levels of brightness and contrastcould be varied between 0–100 using on screen manager(OSM), which is the monitor’s digital control system.

Noncontact measurements were performed using a spec-troradiometer CS-1000 of Minolta. CS-1000 was focusedon the center of the monitor screen with a measuring area of1.6 cm in diameter. Target colors were displayed on acentral square patch of 2.43 2.4 cm larger than the mea-suring area. The remainder of the display was set to aluminance factor of 0.2 relative to the peak white.5 Theminimum luminance that could be measured is on the orderof 0.01 cd/m2 and the accuracy is6 2% in luminance (forCIE Illuminant A). All measurements were performed in adark room. Warm-up time to stabilize after initial power-upwas above 2 h and image stabilization time was set 2 minafter an image change.

RESULTS AND DISCUSSION

First, we tested the change ofg according to brightness andcontrast control in the LG monitor. For 35 combinations of

FIG. 3. Normalized luminance vs. DAC count for 5 differentamplifier offset settings, when gain and gamma are fixed.

FIG. 4. DAC count that yield constants A of 0.25 vs. offsetfor 3 different gains.

FIG. 5. Change of gamma (g) according to brightness andcontrast for LG.

TABLE I. Estimated gamma using nonlinear optimi-zation subroutines of ORIGIN for the combinations offive levels of brightness and two levels of contrast.

Contrast/Brightness B30 B40 B50 B60 B70

C50 2.614 2.584 2.538 2.526 2.512C70 2.460 2.436 2.457 2.453 2.466


5 levels of brightness (30, 40, 50, 60, and 70) and 7 levelsof contrast (20, 30, 40, 50, 60, and 70), 17 neutrals fromblack to white were measured to form the tone reproductioncurves. Using nonlinear optimization subroutines of ORI-GIN, normalized system offset, gain, andg parameters werestatistically estimated. Figure 5 shows the change ofgaccording to brightness and contrast control. The length of

the bar shows the difference ofg for 5 levels of brightnesswhen the contrast level was fixed. The difference decreasesas the level of contrast increases. Above contrast level of 50,the length of the bar becomes comparably shorten and theaverageg for 5 levels of brightness converged to a partic-ular value. This value would be expected as an inherentgamma coefficient for RGB channels, if white balance wasachieved successfully during manufacture. When consider-ing this aspect, it is advantageous to select high contrastlevels. On the other hand, because the slope of lines in Fig.4 is inversely proportional to gain, there is little differencein the slope of the line between the high contrast levels.

FIG. 6. Luminance of 5 neutrals measured at 3 differentlevels of brightness in combination with the contrast level of50 and 70 for LG.

FIG. 7. DAC count that yields constant A of 0.06 vs. bright-ness level for 2 different contrasts for LG.

FIG. 8. Normalized luminance vs. normalized DAC count inlog scale for red, green, blue, and neutral measured fromLG’s optimum setting of B56C95.

FIG. 9. Change of gamma according to brightness andcontrast for Samsung.


Therefore, two levels of contrast should be selected properlywhen considering both aspects.

Table I shows the estimatedg for 5 levels of brightnesswhen the two levels of contrast are 50 and 70. Yet there aresmall differences ing between brightness levels. Thesedifferences would make a straight line into a smoothlycurved line in Fig. 4. Therefore, more than two data areneeded to interpolate the curved line and the second-order

polynomial fitting would be needed. Also, there is a differ-ence in g between the two levels of contrast for eachbrightness level. With this difference, the intersection pointof two curves is miscalculated, which introduces greatererror in the range of the high DAC counts.

The arbitrary constant value ofA, needed to computeDAC counts using Eq. (3) was chosen to 0.06, so thatrelatively low DAC counts would result. The luminance for6 tones of neutral: (47,47,47), (63,63,63), (79,79,79),(95,95,95), (111,111,111), and (255,255,255), were mea-sured and normalized with the luminance of peak white. Sixsettings were selected out of the combinations of threelevels of brightness (30,50,70) and two levels of contrast(50,70). The measured normalized luminances are shown inFig. 6.

From Fig. 6, the DAC counts that yield constantA of 0.06can be obtained using a second-order polynomial fitting foreach curve. The plots of the DAC counts against the bright-ness level for two levels of contrast are shown in Fig. 7.Because the radius of curvature of each line is very large,the second-order polynomial fittings with three data areachieved successfully, as shown in Fig. 7. With the twofitting functions, the optimum brightness level was calcu-lated at 56. At that brightness level, the level of contrast wasdetermined to 95, in which the luminance of peak white isjust below saturation. With a brightness level of 56 and acontrast level of 95, the LG monitor could be set to itsoptimum setup.

These optimized adjustments can be examined by mea-suring red, green, blue, and neutral tones displayed on themonitor, in which corresponding DAC counts were steppedfrom 15 to 255 in increments of 16. Figure 8 shows thenormalized luminance vs. normalized DAC count in logscale. For all colors except blue, the interpolated data form

FIG. 10. Luminance of 5 neutrals measured at 3 differentlevels of brightness in combination with the contrast levelsof 50 and 70 for Samsung.

FIG. 11. DAC count that yields constant A of 0.08 vs.brightness level for 2 different contrasts for Samsung.

FIG. 12. Normalized luminance vs. normalized DAC countin log scale for red, green, blue, and neutral measured fromSamsung’s optimum setting of B43C90.


nearly straight lines, from which the optimum setup can beconfirmed. However, for blue, data for the 15 DAC countdeviated from the straight line. Because the luminance ofblue is much less than red or green, it would be moredifficult to adjust the offset of the blue channel compared tothe other channels in the white balance process. This aspectmight be caused by a lack of white balance during manu-facture. Therefore, this setup can be considered as optimum,in which the offsets for all the channels are nearly zero.

Next, we tested the Samsung monitor. The change ofgaccording to brightness and contrast control is shown inFig. 9. The difference ofg for five levels of brightness isalmost the same for any contrast level, which is verydifferent from LG monitor. However, the averageg forall brightness levels approaches closer to a particularvalue as the contrast level increases, which is similar toLG monitor. Therefore, two levels of contrast were se-lected at 50 and 70, equal to the LG monitor, and threelevels of brightness were selected as 20, 40, and 60. Theluminance for 6 tones of neutral were measured andnormalized, as shown in Fig. 10.

The DAC counts that yield constantA of 0.08 can beobtained using second-order polynomial fittings for eachcurve. Figure 11 plots the DAC counts vs. brightness levelfor two levels of contrast. With the same procedure as forthe LG monitor, the Samsung monitor can be set to itsoptimum setup with a brightness level of 43 and a contrastlevel of 90. Also, Fig. 12 shows the measured normalizedluminance vs. normalized DAC count in log scale for red,green, blue, and neutral. This figure shows a similar result tothat of the LG monitor.

Because the lines shown in Figs. 8 and 11 were nearlystraight for all DAC counts except 15 DAC, the gammacoefficient of each channel can be determined from the ratioof any two measuring data by taking the logarithm of boththe normalized luminance and the normalized DAC count.For the two monitors, the gamma coefficients determined by255 DAC and 127 DAC for each channel are shown inTable II. For the LG monitor, all gamma coefficients for theRGB channels are very close to a convergent value, shownin Fig. 5. On the other hand, in the case of Samsungmonitor, only two gamma coefficients are closer to a con-vergent value, shown in Fig. 8. The gamma coefficient ofthe red channel is not consistent. This could be explainedwith the lack of white balance. From these results, it mightbe concluded that the gamma coefficients determined usingour technique could be regarded as the inherent gamma ofeach display system.

With these gamma coefficients, tone reproductioncharacteristics of the RGB channels could be character-ized with the following simplified equation without offsetand gain:

L

Lmax5 S d

2N 2 1Dg

. (4)

For each monitor, the luminance differences between thepredicted and measured data for the three channels wereplotted against the normalized DAC count in Figs. 13(a)and (b), respectively. For all monitors, the largest resid-

FIG. 13. Residual normalized-luminance error betweenmeasurement and prediction for tone reproduction of RGB:(a) LG, (b) Samsung.

TABLE II. Determined gamma coefficients for red, green, and blue channels and CIELAB color differences for125 colors.

Monitor

g DE*ab

R G B AverageStandarddeviation Minimum Maximum

LG 2.451 2.490 2.477 0.46 0.20 0.05 1.01Samsung 2.485 2.348 2.366 0.75 0.26 0.05 1.30


ual error occurred in the green channel were within20.006 for data ranging between 0 –1.0. It might beassumed this would have a small impact on the colorreproduction.

In order to demonstrate the insignificance of thesedifferences, the 125 colors were tested. The DAC countsfor the individual channel were 255, 223, 191, 127, and0. With the determined gamma coefficients and a singletransformation matrix5 based on the maximum red, green,and blue, the tristimulus values of the 125 test colors canbe predicted. CIELAB color differences were calculatedbetween measurements and predictions, where the mon-itor peak white was used to defineXn, Yn, andZn in theCIELAB equations. The mean, standard deviation, min-imum, and maximum color difference for each monitorare shown in Table II. The LG monitor had an averageaccuracy of 0.46DE* ab with values ranging between0.05–1.01DE* ab. However, the Samsung monitor hadsomewhat larger color differences than the LG monitor.This error could be explained by the RGB channel’sindependence. Table III shows the comparison betweenthe sum of measured luminances for RGB displayedindividually and the measured luminance for the displaywhite. The larger difference in the Samsung monitormight yield the larger color difference. Figures 14(a) and(b) show the distribution of color differences as a func-tion of L* of the 125 test colors for each monitor,respectively.

CONCLUSION

This research was about a technique to set the optimumbrightness level, in which offsets for RGB channels areapproximately zero. For the ideal monitor, the optimumbrightness level can be set by measuring a few tones ofneutral for the combination of any two levels of brightnessand any two levels of contrast. However, in practice, thegchanges according to the brightness and contrast controls.The change ing would bring nonlinearity to the relationshipbetween DAC count and brightness level.

In this study, theg changes according to the brightnessand contrast controls were analyzed thoroughly for twomonitors. The amounts of change according to brightnesscontrols at a fixed contrast are different from monitor tomonitor. However, the averageg for all brightness controlsconverged to a particular value of each monitor at highlevels of contrast. From this, we found out that the nonlin-earity of the relationship between DAC count and bright-

TABLE III. Measured luminance of red, green, blue, and white, and the sum of the RGB primary luminance.

MonitorRed

[cd/m2]Green[cd/m2]

Blue[cd/m2]

White[cd/m2]

Sum(R 1 G 1 B)[cd/m2]

Difference[%]

LG 27.44 76.75 11.32 115.70 115.51 0.16Samsung 24.28 78.52 9.50 114.60 112.30 2.01

FIG. 14. CIELAB color differences as a function of L* for125 colors: (a) LG, (b) Samsung.


ness level can be minimized, if high levels of contrast areselected. And the second-order polynomial fitting is suffi-cient to fit the smoothly curved line with data measured atthree levels of brightness.

The optimum brightness setup has been achieved suc-cessfully, and inherent gamma coefficients of RGB chan-nels can be determined. With these gamma coefficients,tone reproduction characteristics of RGB channels can becharacterized with the simplified equation, neglecting offsetand gain parameters. The accuracy of characterization isbetter than 0.5DE*ab for 125 colors for a monitor havinggood channel independence.

It is a very convenient technique with two advantages.One advantage is the measurement instrument. Because itdoes not require measurements for 0 DAC count and chro-maticity, high-precision instruments are not necessary.The other advantage is the math. It does not requirenonlinear optimization. Gamma coefficients can be easilycalculated from the log–log relation with only two mea-suring data. However, this technique is practical formonitors having digital brightness and contrast controls.It may be difficult and unreliable to adjust levels withanalog controls.

ACKNOWLEDGMENTS

This research was supported by the Center for Educational–Industrial Cooperation of Daejin University.

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optimum brightness level and simplified characterization of crt color monitors

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